This article is cited in 9 papers

On Irreducible Representations of Discrete Heisenberg Groups

S. A. Arnal', A. N. Parshin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We prove that the irreducible representations with finite weight of discrete nilpotent groups of class $2$, including the discrete Heisenberg groups, are monomial representations and obtain their classification for the group $\operatorname{Heis}(3,\mathbb Z)$.

Keywords: discrete Heisenberg group, discrete nilpotent group, monomial representation, representation of finite weight.

UDC: 512.544.33

Received: 06.12.2011

DOI: 10.4213/mzm9289

 English version: Mathematical Notes, 2012, 92:3, 295–301

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